


Bulletin 8 



T J 

3 



* 



DEPARTMENT OF THE INTERIOR 
BUREAU OF MINES 

JOSEPH A. HOLMES, Director 



THE FLOW OF HEAT 
THROUGH FURNACE WALLS 



BY 



WALTER T. RAY and HENRY KREISINGER 




WASHINGTON 

GOVERNMENT PRINTING OFFICE 

1911 



M 



±r£h 





(lass T 5 3 £ 

Book ,"R 3 



Bulletin 8 



DEPARTMENT OF THE INTERIOR 
fj.$ BUREAU OF MINES 

JOSEPH A. HOLMES, Director 



THE FLOW OF HEAT 
THROUGH FURNACE WALLS 



BY 



WALTER T. RAY and HENRY KREISINGER 




WASHINGTON 

GOVERNMENT PRINTING OFFICE 
1911 



ot I 



o 

CONTENTS. / 



Page. 

Introduction 3 

Acknowledgments 4 

Equipment and methods 5 

Construction of furnace 5 

Position of thermocouples 5 

Construction of thermocouples 7 

Headings . 7 

Discussion of temperature curves 8 

Equilibrium of furnace- wall temperatures 9 

Temperature drops in furnace walls 10 

Resistance of fire brick, air space, asbestos, and common brick 11 

Conclusions 19 

Discussion of physical laws 20 

The law of radiation 20 

The law of heat conduction 24 

Comparison of the laws 27 

Application of the laws 30 

Publications on fuel testing 31 



ILLUSTRATIONS. 



Page. 
Figure 1. Elevation and plan of furnace 6 

2. Vertical sections of furnace; through stoker and through long com- 

bustion chamber „ 7 

3. Construction of furnace walls and position of thermocouples 8 

4. Construction of furnace roof and position of thermocouples 9 

5. Temperatures of furnace wall and roof (thermocouple sets b and c) . . 11 

6. Temperature drops through furnace wall and roof (thermocouple 

sets b and c) 12 

7. Temperatures of furnace wall and roof (thermocouple sets d and e) 

and gas temperature 13 

8. Temperature drops through furnace wall and roof (thermocouple 

sets d and e) 14 

9. Temperatures of furnace wall (thermocouple set a) 15 

10. Temperature drops through furnace wall (thermocouple set a) 16 

11. Temperature drops through furnace wall and roof (thermocouple 

sets a, b, c, d, and e) 18 

12. Radiation of heat from a hot spheroidal surface to an inclosing cooler 

surface 22 

13. Radiation of heat from infinite hot plane surface to infinite cooler 

plane surface 22 

14. Radiation of heat from hot plane surface to convex surface 23 

15. Radiation of heat from a hot surface to an infinite cooler surface at 

various temperatures, relations expressed in the metric system of 
units 24 

16. Radiation of heat from a hot surface to an infinite cooler surface at 

various temperatures, relations expressed in the metric system of 
units 26 

17. Radiation of heat from a hot surface to a cooler surface, relations 

expressed in British thermal units, degrees Fahrenheit, and square 

feet 28 

18. Radiation of heat from a hot surface to a cooler surface, relations 

expressed in British thermal units, degrees Fahrenheit, and square 

feet : . . . 29 

19. Comparison of laws of heat radiation and heat conduction 30 

2 



if ^w JUZJ n -i 






THE FLOW OF HEAT THROUGH FURNACE WALLS. 



By Walter T. Ray and Henry Kreisinger. 



INTRODUCTION. 

This bulletin contains a statement of certain results that will be 
embodied in a report describing investigations of the combustion of 
fuel made by the United States Geological Survey and the Bureau of 
Mines in a specially constructed long furnace. The furnace forms 
part of the fuel-testing plant at Pittsburg, Pa., which was established 
and equipped by the Geological Survey, but passed under the control 
of the Bureau of Mines on July 1, 1910, when a transfer of fuel-test- 
ing investigations, authorized by act of Congress, became effective. 
The work discussed in this bulletin was done under the direction of 
the Geological Survey. 

The furnace was designed and built for an experimental study of 
the processes of combustion, this study being part of a comprehen- 
sive plan for testing fuels to determine their heat value and the man- 
ner in which they can be used to best advantage. Although the 
main object of the researches made with the furnace by the Geological 
Survey was to examine critically the production of sensible heat by 
combustion along the path of the gases rising from the fuel, an inter- 
esting as well as important side problem developed in the study of 
the simultaneous dissipation of the heat through the walls and roof 
of the furnace. Thus incidental data were collected on the tempera- 
ture gradient through the walls at several places. These temperature 
data (together with the heat conductivity of the material of the walls) 
formed the basis for calculating the heat dissipated through the walls. 

The object of this report is to present and discuss these tempera- 
ture data. The discussion particularly concerns the air-space type of 
wall construction as compared with the solid brick wall or walls type, 
in which the air space is filled with some solid material of low heat 
conductivity. The conclusion of the authors, which perhaps will sur- 
prise some readers, is that, so far as loss of heat is concerned, a solid 
wall of brick or any ordinary material is preferable to a hollow wall 
of the same total thickness, especially if the air space in the hollow 
wall is near the furnace side. 

There is a general belief that since air is a poor conductor of heat, 
air spaces built into the walls of a furnace will prevent or reduce heat 
dissipation through the walls. Although there may be instances of 



4 FLOW OF HEAT THKOUGH FURNACE WALLS. 

furnace walls in which such construction reduces the rate of heat flow 
through them, yet as a rule the effect of the air space is just the oppo- 
site. While the heat does travel very slowly through the air by con- 
duction, it leaps over the air space readily by radiation. Although 
this latter mode of heat propagation is common in nature, the laws 
governing it are not generally known and are seldom taken into con- 
sideration when furnace walls are being designed. 

It may be stated here that the quantity of heat passing through a 
portion of a solid wall by conduction depends on the difference between 
the temperatures of the two planes limiting the portion of the wall. 
The quantity of heat that passes across the air space in the wall de- 
pends on the difference of the fourth powers of the absolute tempera- 
tures of the surfaces inclosing the air space. It follows that, in case 
the heat passes by conduction through the solid portion of the wall, 
the loss remains approximately the same so long as the temperature 
of the two limiting planes remains constant, no matter what may 
be the temperature of the two planes. On the other hand, the heat 
passing across the air space by radiation increases rapidly with the 
temperatures of the inclosing surfaces, although the difference between 
these temperatures may remain constant. This feature will be shown 
by curves in the latter part of this paper and thoroughly discussed. 
The important point is that the air space, which is advantageous in 
the walls of a refrigerator because the temperatures are low, is objec- 
tionable in a furnace wall because the temperatures are high. 

It is customary to put air spaces in furnace walls between the fire- 
brick linings and the common brick. Usually the fire-brick lining is 
only half a brick thick, which construction brings the air space too 
close to the furnace. The result is that the temperatures of the sur- 
faces inclosing the air spaces are too high, and in consequence too 
much heat is radiated across the spaces. The heat passing through 
such walls would be much reduced if the air spaces were filled with 
brick, or, better, with some cheap nonconducting materials, such 
as ash, sand, mineral wool, etc. Even where the fire-brick lining is 
one brick thick (9 inches), the temperature in the furnace may be 
high enough to raise the temperatures of the air-space surfaces so 
much that the heat radiated across the space will amount to more than 
would the heat conducted through a filling, were the filling only com- 
mon brick. This last statement is amply justified by the data here 
presented. 

ACKNOWLEDGMENTS. 

The authors wish especially to thank John K. Clement, physicist, 
and his assistant, L. H. Adams, both now of the Bureau of Mines, 
for their aid in devising methods, taking many of the observations, 
and assisting the authors in studying the data. 



FLOW OF HEAT THROUGH FURNACE WALLS. 5 

EQUIPMENT AND METHODS. 
CONSTRUCTION OF FURNACE. 

The specially constructed furnace is about 43 feet long over all. 
At one end is a mechanical stoker; at the other the gases from the 
combustion chamber discharge into a water-tube boiler. The com- 
bustion chamber is a tunnel 3 feet wide, 3 feet 3 inches high, and 
about 35 feet 6 inches long, with double walls and arch roof. The 
inner walls and the inner arch are 9 inches thick and are of best 
quality fire brick. The outer walls, 8 inches thick, are of common 
and pressed brick. The outer arch, 4 inches thick, is of repressed 
brick. In the sides a 2-inch air space separates the two walls; in the 
roof a 1-inch layer of flake asbestos separates the two arches. Air 
leakage through the walls and roof is minimized by using blowing 
and exhaust fans to keep the interior of the chamber as nearly as 
possible at atmospheric pressure. 

POSITION OF THERMOCOUPLES. 

The data presented in this bulletin consist of three sets of measure- 
ments of temperatures at four different depths in a side wall of the 
furnace, and also of two sets of measurements in the roof. The 
material of the outer wall and arch is, for convenience, designated 
common brick in the discussion of the data. 

Figure 1 presents the elevation and the plan of the special fur- 
nace as it was at the time of getting the data given in this report. 
Figure 2 gives vertical sections of the furnace. Figure 3 shows the 
positions of the thermocouples in the side wall at places denoted in 
figure 1 by a, b, and d. Figure 4 gives the construction of the arch or 
roof of the furnace and the location of thermocouples at places c and 
e. No couples were inserted in the roof corresponding to location a 
in the side wall, because it was feared that the lower side of the lining 
had been melted away considerably. 

The thermocouples were placed in f-inch holes, which were drilled 
in the wall and the roof after the furnace was built. The holes were 
intended to extend within 1 inch of the outer and inner surfaces of 
the wall and the roof, as indicated in figures 3 and 4. The depths 
of the holes for couples 1 and 3 could be measured accurately, and 
therefore these couples were put at known depths, as represented in the 
figures. The distances of the ends of the holes for couples 2 and 4 
from the inner surfaces could not be accurately measured, so that 
the distance given in the figures are only approximate. Each couple 
was placed in such a way that the fused junction touched the bottom 
of the hole. Near the outer surface of the wall the annular spaces 
around the wires of the couples were filled with asbestos packing as 
deeply as possible, in order to prevent radiation of heat from the 



6 



FLOW OF HEAT THROUGH FURNACE WALLS. 



j3|iog 



55 




H 







YW'M'Su 






i/JFriSr'A r„vA'A* ui/ryvi/i V l/,/»u\ ■/■ 



EQUIPMENT AND METHODS. 7 

couples and from the bottom of the holes, and also to stop the cool- 
ing of the couples by any current of cold air that might be drawn 
around the couples into the furnace. This precaution was more 
effective with thermocouples 1 and 2 than with thermocouples 3 and 
4, because the packing could not be put around the couples in the 
inner fire-brick wall. Consequently, the indications of these couples, 
and particularly of thermocouple 4, are not exact and should 
always be considered as approxi- 
mate. 

CONSTRUCTION OF THERMO- 
COUPLES. 

The thermocouples were made 
of wires about 1.5 mm. (^ inch) 
square, and were obtained from 
the Hoskins Manufacturing Co., of 
Detroit, Mich. The terminals of 
the thermocouples were soldered 
to copper leads, the joints being far 
enough away from the embedded 
junctions to insure 
their being approx- 
imately at atmos- 
pheric tempera- 
ture. All other 
connections in the 
leads were soldered. 
Each couple was so 
connected that it 
could be thrown 
into series with a 
galvanometer by a 
snap switch. Con- 
sequently it was 
possible to get the 
twenty readings 
within about a 
minute. The couples proved durable and dependable up to 1,400° C. 
(2,552° F.) and were not much changed by exposure at such tem- 
perature to furnace gases and dust. 



-re'- 




p 9' 4- >i 

Figure 2.— Vertical sections of furnace, through stoker and through long 
combustion chamber. 



READINGS. 



Inasmuch as all readings were relative, no attempt was made to 
get the temperatures closer than 2 or 3 degrees; moreover, any 
greater accuracy in the couples and instruments would have been 



8 



FLOW OF HEAT THROUGH FURNACE WALLS. 



useless, because the bricks containing the holes might have been 
more porous than others, or some of the holes might have opened 
into cracks; the holes could not well be inspected. Therefore, the 
worth of the readings lies as much in their rates of change as in their 
actual values at any time. 

The sets of thermocouples in the side wall are designated a, b, and 
d, and the sets in the roof are designated c and e. The couples 
in each set are numbered from 1 to 4. The reading of any thermo- 
couple is referred to by the letter of the set, with the number of the 
couple as subscript. 

The temperature readings of the thermocouples embedded in the 
wall and roof were taken on a number of tests. 

INSIDE 



Fire brick 



r 



11 



Fire clay, 



Fire brick 



Air space 



Common brick 



Mortar\ 



Repressed 
face brick 



JNo.4 



_.i 



No:3 



|!No.2 
i 3 i" 



4J 



•jNo.1 



NT 

I 



I 

I 
l 
1 



si 
CM 



1 

1 
1 
1 



1 

1 



OUTSIDE 

Figure 3. — Construction of furnace walla and position of thermocouples. 



DISCUSSION OF TEMPERATURE CURVES. 

The readings of test No. 16 are platted in figures 5, 7, and 9. This 
test is a fair representative of other tests in which complete sets of 
wall and arch readings were obtained every 20 or 30 minutes through 
the entire test of 29 hours' duration. The test was run until the 
wall temperatures reached equilibrium, that is, until they ceased 
to increase. The readings were platted on time as abscissae, so that 
the slopes of the curves show the rate of change. 

Figure 5 shows the temperature readings for the entire test of the 
thermocouple sets placed at b and c. (See fig. 1.) This chart shows 



DISCUSSION OF TEMPERATURE CURVES. 9 

that, excepting perhaps within 1 or 2 inches from the inside of the 
furnace, the brickwork is nearly cold when the test is started, and 
that as the heat flows out through the wall from the inner surface 
the temperatures of the portions of the wall farther from the furnace 
rise for about 19 hours of the test, after which period the equilibrium 
of wall temperature is reached. Up to this time most of the heat 
entering the wall goes to raise the temperature of the latter; there- 
after all the heat entering the wall goes through it and is lost by 
radiation. 

EQUILIBRIUM OF FURNACE-WALL TEMPERATURES. 

In the following discussion the nearly true assumption is made 
that there is no cooling effect due to leakage currents of air through 
the brickwork or into, out of or along the air space. 

TOP 




INSIDE 

Figuee 4. — Construction of furnace roof and position of thermocouples. 

During the equilibrium, the quantity of heat passing through an 
inner part of the wall is exactly equal to the heat going through 
another part farther out. For example, the quantity of heat which 
is conducted through the inner fire-brick wall is exactly equal to the 
heat which passes across the air space, and is exactly equal to the heat 
which is conducted through the outer common brick wall, and also 
equal to the heat radiated or taken in any other way from the out- 
side surface. If this equality of heats did not exist, the equilibrium 
would be impossible. For example, let it be assumed that more heat 
passed through the inner than through the outer wall and over the 
air space; then the heat would accumulate near the surface next to 
the air space and the temperatures shown by thermocouples 3 would 
be rising, a circumstance opposed to equilibrium. Again, let it be 
68820°— Bull, 8— 11— 2 



10 FLOW OF HEAT THKOUGH FURNACE WALLS. 

assumed that more heat passed through the outer wall than through 
the inner one and through the air space; in that case the heat in 
the outer wall near the surface next to the air space would diminish 
and the temperatures shown by thermocouples 2 would drop, an 
event that would be contrary to the equilibrium conditions. The 
statement that during equilibrium of the wall temperatures in any 
cross section of the wall the quantity of heat passing through one 
part of the section is exactly equal to the quantity passing through 
any other part is therefore justified. 

TEMPERATURE DROPS IN FURNACE WALLS. 

The quantity of heat flowing by conduction from one plane to 
another through any portion of the furnace wall depends upon the 
difference of temperature between these two planes and upon the 
resistance to the heat flow. With the same temperature difference, if 
the resistance is high, a small quantity of heat flows through; if the 
resistance is low, a large quantity flows through. Or, if the quantity of 
heat is to remain constant the temperature difference must be large if 
the resistance to the heat flow is high, and small if the resistance is low. 

So, in the case of the furnace wall, where the quantity of heat 
passing between any two planes which are parallel to the surfaces of 
the walls is the same, the temperature difference between any two 
planes indicates the resistance which the material or space between the 
two planes offers to the flow of heat. For example, if the temperature 
difference between the faces of the fire-brick wall is high, it may be 
said that the resistance to the heat flow of the fire-brick wall is high; 
or, if the temperature difference between the two surfaces on each 
side of the air space is low, it may be inferred that the resistance to 
the heat passage across the air space is low. Thus it is possible to 
rely on the temperature difference as being a true indicator of high or 
low resistance to heat flow between any two planes which are parallel 
to the surface of the wall. With this knowledge the reader can turn 
to the charts and study the resistances of the fire brick, the air space, 
the asbestos layer, and the common brick, and the relative value of 
these materials as heat insulators in the construction of furnace walls. 

Figure 6 gives the temperature drops through the side wall as 
recorded by the set of couples placed at h, and through the roof as 
recorded by the set of couples placed at c. At the foot of the figure 
is shown diagrammatic ally the thickness of the side wall, and at the 
top of the figure is shown the thickness of the roof; in each case the 
measurements of thickness are used as abscissae in the chart. The 
temperatures at the various points are platted as ordinates. The 
figure shows three temperature gradients or drops through the wall 
and through the roof, one at 11 a. m., April 12, when the test was 
started, one at 4 p. m. the same day, and one at 2 p. m. the next day. 
The first two gradients give the relation of the temperatures before 



DISCUSSION" OF TEMPERATURE CURVES. 



11 



the equilibrium is reached, and are interesting only when compared 
with one another to show how the temperatures change with respect 
to each other while the walls are being heated. The last gradient 
represents the equilibrium and is of most interest. 



o 



TEMPERATURES.°C 



a 



F3 

S 

O) 

•vl 
09 

o 



irx 



\\ 



.^ 



i 



v\ 



>N 



\ 



r 



A 



T 



X 



\ 



i»! 



$ 



\\ 



I 



\ \ 



VV 



'V 



T7 



y 



/ 



-X 



' 1' 
i h 



J 



^ 



i )i 



!? 



?x 



y 



■H 



s 

en 

> 

-a 

CD 
<0 



\ 



-T- 



\ 






5?I?11S 



M » Co 



M 






41 



; 



7" 



/ 



A- 



V 



^v 









«- 



-^w- 



M 



11 



ij 



I ll 



O OCT 
— N — 



C OCT 



O 



CT 



RESISTANCE TO HEAT PLOW OP FIRE BRICK, AIR SPACE, ASBESTOS, AND COMMON BRICK. 

The striking feature concerning the side-wall thermocouples, set 6, 
is the large temperature drop through the fire-brick wall, the very 
small drop through the air space, and, again, the large temperature 



12 



FLOW OF HEAT THROUGH FURNACE WALLS. 



drop through the common brick wall. These drops plainly indicate 
that the resistance to heat passage of the air space is very low Cora- 



ls 
W 

A 

£h 



THICKNESS OF ARCH ROOF, INCHES. 
4 6 8 10 12 14 , 



1000 



900 



800 



P 700 



m 

p-i 

p 
o 
o 
o 

« 
w 
W 

En 



600 



500 



400 



300 



200 



5 100 

CO 

«! 

N* 

O 

O 

H 
ft 

i—i 

CQ 
ft 

o 

CQ 

P 

EH 

H 
Eh 



900 



800 



700 



600 



500 



400 



300 



200 



100 



v// 


I 


Fire brick. 


1 


I 


i 


sbes- 
tos. 


Re 


pressed 
brick 














































































"c' 


cc 


up 


es. 






















































N 5 


\4 






































v5 


^» 




^ 


\ 


































^V 


fo 


^ 




































N? 










































^ 


£ 
































































































































































































S *' 


\5 


> 

V? 




































Y* 


& 

Sr 


> 
































\> 


















' 


b" 


CO 


ipl( 


»s 4 














V 


"5s 

1^ 








































\"v 























































































































































/// 


m 


Fire 
y ///V//y 


bri 


ck. 




^ 


Airspace. 

m i t^ 


Common and repressed 



4 6 8 10 12 14 16 

THICKNESS OF SIDE WALL, INCHES. 



18 



ft 



20 



pared with that of either brick wall, only about one-fourth as 
much. The last temperature gradient through the roof, as given by 



DISCUSSION OF TEMPERATURE CURVES. 



13 



the set of thermocouples c, shows a rather low temperature drop 
through the fire brick, a high drop through the 1-inch layer of asbestos, 
and a rather small drop through the common brick. These tempera- 



TEMPERATURES,'°C. 





_. ro a . 
o o o < 

o O O O ( 


1200 
1T00 
1000 
900 
800 
700 
600 
500 




iyn t 












\ 


^ 

1 

^ 








.. 




ro 


fc 


V 
\ 












\ 


\ 
t 
i 






':• 




*t\> 


II 
















/ 










? 




k \ 












t 












1 "? 


V i 




\\ 










\ 


\ 






.-'• 






\ 


\\ 










\ 




















... 1 1 


\ 

1 


Y\ 








£ 





- , \ 










4 * 
1 

1 o, 


it v 


\ 
1 

\ 




\ 










Y 






) 




) i 




■ * 


\ 
\ 










I 

V 












R 1 




\ 


L\ 










ii 










m 

o 


V, 

i. 




\ 
\ 


1 v 

i \ 










\ 






••._ 




g> o 


i 
* 




\j 


\ 




















3 St 


il 


i 


\ 


-, \ 








i / 


y 










s> .ro 


3 


i 
1 




\ 

t i 


1 
i 
I 






V 1 

>4 












p 




; ■ 


1 

2 > ro 


i 
1 


j 




\\ 


\ 














*\ 




o 2 

>-4> 


i 
i 


1 
! 




IN 


i 








1 










4- 
Ap 

thermocc 


i 

i 


\\ 




W 


■ i 
\ 








II 










1 
i 

i 


ii 




\) 


1 








<l 




.•' 






C 3. 


~1 

i 


1 




x 










2 




" 








1 

i 


II 




l\ 

1 1 
M 








(' 


/ 

i 










8 
d and c) 


1 


ii 




V, 








y 1 


i '.'i 










i 


i! 
■I 




/) 

.'1 










X 










P. _ 


i 
i 


i 




[j 
















"**: 




g 


i 
i 


!! 




IT 










\ i 








• 




• 




| 


/I 
1 1 




i 1 










)\ 






# «" 




g tv 

p 


1 


!! 




i | 










) 










to 


! 


||. 




i l 
i i 

| 1 


\- 














'••... 




? 


I 


1 1 

li 




1 i 


V 

i 








1 






•. 




* 




jl 




i 


1 
i 








; / 
} » 






LO t> 




£? 


cd a. 

P0-* 




CD Q. Q. 

co ro c*> 








CD CL 
















^ 


















• 


















































f.i 





ture drops indicate that the resistance to heat flow of the 1-inch 
asbestos layer is higher than that of 7 inches of fire brick. By com- 
paring the last gradient of couples b with that of couples c, it is easy 



14 



FLOW OF HEAT THROUGH FURNACE WALLS. 



to see that 1 inch of asbestos is much more effective as a heat insulator 
under the existing conditions than a 2-inch air space. Although the 



THICKNESS OF ARCH ROOF, INCHES. 
4 6 8 10 12 14 



1000 



900 



800 



O 



700 



500 



w 

P 

Ph 600 

O 

o 

o 

P 400 



pq 



300 



200 



P 100 
02 

<j 

g" 

c 

PS 

p 

< 
p 

t 
a 

02 

o 

02 

W 500 
H 

P 
Ei 

< 

Ph 
3 

Eh 



900 



800 



700 



600 



400 



300 



200 



100 



%/ 

^ 


1 




mmmm 


1 


1 






w 


/ ///)y/// 




















F] 


re 1 


>ric 


k. 




A 


sbe 
tos 


S- 


Re 
1 


pressec 
jriek. 


I 




































































































\^ 








































\* 


• 


* 












"e" 


COl 


apk 


!S. 




















^ \*a' 




































^ 
*? 






) \ 




































\ 


<A 








































v>\ 


























— 
























































































































































































































^ 








d 


CO 


upl 


es. 


























& 


^ 


EJi 










































































^ 


& 


4j 




































^ 


1.JJ 


^T 
































u 


gr-ia. 
















^ 


Fire brick. 


m 


M 


1 


Air spac 

1 1 


, Common and repressed 





T3 
PI 

t3 



A 

Ml 
O 



00 

6 



18 



20 



2 4 6 8 10 12 14 16 

THICKNESS OF SIDE WALL, INCHES. 

total thickness of the roof is 5 inches less than that of the side wall, a 
smaller quantity of heat per square foot is lost through it than 



DISCUSSION OF TEMPEEATUEE CUEVES. 



15 



through the side wall. The relative amounts of heat passing through 
the two constructions can be figured approximately in the following 
manner : 

TEMPERATURES, °C 





o 


— tv> 
§ § 


■ 


to 

5 


o o 


O) ~J CD < 
C3 O O < 

o o o < 


1200 
1100 
000 






\ 


























ro 




\ 






' 




















^om 




\ 


























? 






























> 




\ 


























i\> 
































| 








_T 




























\ 




























_^ 


























\ 


\ 
















H 




























1 

t-3 








iz 




i 
















1 








\ 




\ 
















*2 *> 

>-> 

SO 

<rt- 








I 




















03 >> 




















.M'-i- ' 








2 s " 












I 










1 






3 £ 

O 2. K. 








ZT 




\ 














. 


CD _» 
^ CO 

P 




















z 








/^\ 






















> 






fl> 




















a 








o 
o 
o 








■ 


\ 


1 
















CO 








' ( 




/ 








































• 




"J"* o 




















■ (*£:; 








-"°«r, 




























s 












I 
















1\J 






















































<fr. 








1 






















0) 




QJ 


QJ 










Q) 



























































































Inasmuch as the fire brick in the roof are made of the same material 
as the fire brick of the side wall, the conductivity of the fire brick 
in both places may be taken to be the same; and as the thicknesses 



16 



FLOW OF HEAT THROUGH FURNACE WALLS. 



are the same, the amounts of heat flowing through both per square foot 
per unit of time are proportional to the temperature drops. Thus 
the temperature drop through the fire brick in the side wall is from 
965° C. to 510° C, or 455° C; the temperature drop through the simi- 
lar brick in the roof is from 750° C. to 500° C, or 250° C. The heat 
lost through the side wall is f-f-J = 1.8 times as much as the heat lost 
through the roof. 

In a similar manner one can compute the relative heat losses from 
the temperature drops through the common brick. In the side wall 
this drop through 6 inches of common brick is from 440° C. to 



ft" 1100 

M 
ft 

p 

§ 1000 

o 
3 

M 

h 

w 

Eh 

>h 800 
pq 

P 
ft 
Eh 
<J 
O 

M 

P 

»-l 
CO 

p" 
p 

ft 

P 



900 



700 



600 



500 



400 



ft 

o 

CO 

ft" 
« 
P 
H 
«! 

ft 
ft 

ft 



300 



200 



100 





































1 — 






























































































































































































"a 


' cc 


)up] 


es. 


























^ 


6 
































\ 










^ 


































% 


\f 




« 


































v$ 




^ 


































































































^ 


^ 


] 


'ire 


bri 


ck. 


^ 


^ 


i 

^ 


ir s 


pac 


e. 


Common and repres 
i i brick. I 


sed 









10 



12 



14 



16 



18 



20 



THICKNESS OF SIDE WALL, INCHES. 
Figure 10.— Temperature drops through furnace wall (thermocouple set a). 



130° C, or310°C; and in the roof this drop through 2 inches of com- 
mon brick is from 115° C. to 65° C, or 50° C, which, when corrected 
to the equivalent drop for 6 inches of common brick, gives 150° C. 
According to these figures, the amount of heat lost through the side 
wall is f £# = 2 times as great as through the roof. 

Figure 7 gives the temperature readings for the entire test (No. 16) 
of the thermocouple sets located at d and e (see fig. 1), and also the 
temperature readings inside the furnace as measured by a Hoskins 
thermocouple placed in the center of the furnace. The chart shows 



DISCUSSION OF TEMPEKATUEE CURVES. 17 

that in general the temperature inside the furnace and the tempera- 
ture indicated by thermocouple a 4 rise and fall together, as may be 
expected, the temperature of the wall lagging somewhat. 

Figure 8 gives the temperature gradients at the places d and e at 
exactly the same time as those given in figure 6. The indication of 
these gradients confirms that of the gradients of figure 6, which is that 
under the given conditions the air space offers decidedly less resistance 
to the heat flow than either brick wall and much less than the 1-inch 
layer of asbestos. The relative heat losses through the two construc- 
tions as indicated by the temperature drops of figure 8 are as follows : 

Through the fire-brick portion of the side wall the temperature 
drop is from 880° C. to 475° C, or 405° C; through the similar por- 
tion of the roof the temperature drop is from 840° C. to 340° C, or 
500° C. According to these temperature drops, the amount of heat 
passing through the side wall is f^f = 0.8 of the heat passing through 
the roof. This small ratio is undoubtedly due to the incorrect tem- 
perature indication of thermocouple 3 in set e. Upon examining the 
upper half of figure 8, it is apparent that couple 3 reads too low. 
Very likely, when the thermocouple was being placed some of the 
flake asbestos fell into the hole, partly filling it, so that the junction 
of the couple did not come into contact with the fire brick but with 
the asbestos, which insulated it from the brick. There might also 
have been a crack in the brick, where the hole was drilled, through 
which air was drawn into the furnace around the thermocouple, thus 
cooling it. Or, the hole might have been drilled into mortar between 
two bricks, which mischance would also tend to lower the tempera- 
ture of the thermocouple in question. There was no way to inspect 
the bottom of the hole after it was drilled and the couple placed in it. 
Whatever the cause, it is quite certain that the temperature indicated 
by thermocouple 3 is about 200° C. too low. 

Even with this too low temperature of couple 3, the drop through 
the asbestos layer is much greater than through the air space and 
greater than through the common brick. The relative quantities of 
heat flowing through the roof and the side wall as figured from the 
temperature drops through the common brick are about as follows : 

In the side wall the temperature drop through 6 inches of common 
brick is from 390° C. to 140° C, or 250° C; in the roof the tempera- 
ture drop through 2 inches of common brick is from 130°C. tol00°C, 
or 30° C, which, when corrected to the equivalent for a 6-inch wall, 

250 
is 90° C; the heat flowing through the side wall is -qq- = 2.8 times as 

much as the heat flowing through the roof. 

It should be borne in mind that the temperature indications are 
only approximate and therefore the relative heat losses are neces- 
sarily only approximate. However, three of these approximate 



18 



FLOW OF HEAT THEOUGH FUKNACE WALLS. 



computations indicate that the heat flowing through the side wall 
is about twice as much as that flowing through the roof, and only one 



1000 



900 



800 

d 

o 

W 700 

g 600 

o 

§ 500 



400 



300 



200 



in 100 

<J 

8 o 

P 

fc 900 



800 





H 700 

ft 
i— i 
CO 



600 



CO 

£ 500 
P 

H 

Ph 400 
£a 300 



200 



100 



THICKNESS OF ARCH ROOF, INCHES. 
4 6 8 10 12 14 



^ 


1 


^ 

I 


ire 


bri 


ek. 


fi 


§§ 


Asbe's- 
tos. 


m 

R 


Mil 

epressed. 
brick. 










































































































































































































































































































































































"p 
























































































































































































































































b' 


































1 
















"d 




es. 






































































































p 


09° 


F. 




— 


































i92° 


F. 














































\5^ 


.-A\ 


r 


ire 


aric 


k. 






A 


r s 


J&C 


Common and repressed 
3. I 11 brick, i i _ , v 





10 



12 



14 



16 



18 



20 



$ 



ft 



THICKNESS OF SIDE WALL, INCHES. 

indicates that the quantities of heat are about equal; besides, it is 
fairly certain that the data for this one computation are incorrect. 



DISCUSSION OF TEMPERATUEE CURVES. 19 

Figure 9 gives the temperature readings of the four thermocouples 
located at a. Figure 10 shows the temperature gradients as indicated 
by the four thermocouples a. The time of the temperature readings 
used to draw these gradients is the same as for the gradients in figures 
6 and 8. The same striking feature is shown in figure 10 as in the 
latter two figures; that is, the temperature drop across the air space 
is much smaller than the drop through either brick wall, indicating 
that the resistance of the air space to the heat flow is lower than that 
of solid brick. The figure does not contain corresponding tempera- 
ture gradients for the roof, as the temperatures were not recorded. 

In figure 11 are given the temperature gradients of all five sets of 
thermocouples for test No. 17. All the temperature readings were 
taken within a minute, so that the readings may be considered as 
simultaneous. Each gradient is labeled with a letter referring to the 
particular set of thermocouples with which temperatures were read. 
The indication of these gradients confirms that of the gradients ob- 
tained from test No. 16, which is that the resistance of an air space 
to heat flow is lower than that of either common or fire brick and 
much less than that of asbestos. The average temperature drop 
through the fire-brick portion of the roof is about 350° C, and that 
through the side wall about 450° C. According to these tempera- 
ture drops, the amount of heat flowing through the side wall is 

450 

0^7) = 1.3 times that passing through the roof. 

Attention is again called to the fact that the reading of thermo- 
couple e 3 is incorrect, and, for reasons previously given, very likely 
too low. Nevertheless, the readings as given are greatly in favor of 
the solid insulating material and against the air space. 

CONCLUSIONS. 

The results of the investigation as outlined in this bulletin justify 
the following conclusions: 

In furnace construction a solid wall is a better heat insulator 
than a wall of the same total thickness containing an air space. 
This statement is particularly true if the air space is close to the 
furnace side of the wall, and if the furnace is operated at high tem- 
peratures. If it is desirable in furnace construction to build the 
walls in two parts, so as to prevent cracks being formed by the 
expansion of the brickwork on the furnace side of the walls, it is 
preferable to fill the space between the two walls with some " solid" 
(not firm, but loose) insulating material. Any such easily obtainable 
materials as ash, crushed brick, or sand offer higher resistance to 
heat flow through the walls than an air space. Furthermore, any 
such loose material by its plasticity reduces air leakage, which is an 
important feature deserving consideration. 



20 FLOW OF HEAT THROUGH FURNACE WALLS. 

DISCUSSION OF PHYSICAL LAWS. 
THE LAW OF RADIATION. 

The object of the following paragraphs is to explain, by the appli- 
cation of well-demonstrated physical laws, why the results pre- 
sented in the foregoing pages came out as they did. 

It has been stated that although air is a poor conductor of heat, 
air spaces in furnace walls are not desirable, because the heat leaps 
across the space by radiation. This latter mode of heat travel is 
very common in nature ; for instance, the source of practically all the 
energy on the earth, developed and undeveloped — the heat which the 
earth gets from the sun — comes to it by radiation. Notwithstand- 
ing the commonness of this phenomenon, the true laws of radiation 
remained unknown to science until two or three decades ago, and 
even at present they are becoming recognized only slowly by the 
engineering profession. 

In the past, when radiation was considered in any engineering 
problem, the first-power law was usually used in calculation. This 
faulty law, which was proposed by Isaac Newton, stated that the 
heat radiated from a hot body to a cold surrounding body was pro- 
portional to the difference of their temperatures. About thirty 
years ago Stefan found, however, that at high temperatures Newton's 
law was wrong, and that the radiation was very nearly proportional 
to the difference of the fourth powers of the absolute temperatures 
of the two bodies. Some years later Boltzmann demonstrated 
mathematically that from the principles of thermodynamics the 
fourth-power law should hold exactly for an ideal black body. There 
are, however, no substances in nature which behave exactly like the 
black body. The sooted surface comes very close to it (within 
2 to 5 per cent, depending on the kind of soot) and can be taken for 
all practical purposes as a standard. The fourth-power law, which 
is known as the Stefan-Boltzmann radiation law, is expressed by the 
following equation: 

(1) H = C(Ti 4 -T ? 4 ) 

where H = the net heat exchanged between the hot and cold surface 

per unit of the hot surface per unit of time. 
Tj = the absolute temperature of the hotter surface. 
T 2 = the absolute temperature of the colder surface, which 

surrounds the hot surface. 
C = a constant depending on the units of area and time, on the 

unit in which the heat is measured, and on the scale in 

which the temperatures are expressed. 

If H is expressed in small calories per square centimeter of the hot 
surface per minute and T l and T 2 are expressed in degrees centigrade 
on the absolute scale, then 

7 fi^ 

u; ^ /.ooaiu 100,000,000,000 



DISCUSSION OF PHYSICAL LAWS. * 21 

If H is expressed in B. t. u. per square foot of the hot surface per 
minute and T\ and T 2 are expressed in degrees Fahrenheit on the 
absolute scale, then 

2.66 



(II) C = 2.66xl0- n 



100,000,000,000 



The above constants are good only for sooted surfaces when the 
hotter surface is entirely surrounded by the cooler surface, the con- 
dition being that the hot surface must not "see" anything but the 
cold surface. This condition can be satisfied by either of the two 
cases shown in figures 12 and 13. 

In figure 12 the hot surface is the outer surface of a spheroidal body 
that is inclosed within a larger spheroid, the inside of which forms the 
cold surface. Any square centimeter, A, of the hot surface can not 
"see" anything but the cold surface. 

On this spheroidal body two areas, A, are indicated, with the 
intention of illustrating the fact that the radiating surface may be 
either plane or convex without changing the amount of heat radiated, 
but can not be concave, for then some portions of surface A would 
"see" other hot surface of its own hot body as well as the cold surface. 

In figure 13 the hot surface is a plane; the cold surface is also a 
plane parallel to the first one and infinitely large, so that any square 
centimeter, A, of the hot surface, A, can not "see" anything but the 
cold surface; that is, the angle of "vision" approaches the spherical 
angle of 180°. 

In figure 14 the above conditions are not satisfied, because any 
square centimeter, A, of the hot surface can "see" something else 
besides the cold surface; that is, the angle of "vision" is less than 
a spherical angle of 180°, so that the cold surface does not receive 
all the heat radiated by any portion of the hot surface. 

Heat passing from portion A through angles a and c misses the 
cold surface entirely. Therefore, in such instances as are pictured by 
figure 14 the values for C must be calculated for each solid angle of 
"vision" to each respective cold surface's temperature and coeffi- 
cient of radiation. 

Several curves (figs. 15-18) have been platted to show graphi- 
cally the significance of the Stefan-Boltzmann law. 

The law of radiation and the conditions as presented in the pre- 
ceding paragraphs apply to sooted surfaces only. For surfaces not 
sooted this law must be somewhat modified. For instance, a brick 
surface does not radiate so much heat as a sooted surface of the 
same temperature, nor does it absorb so much of the heat which 
reaches it by radiation. In consequence, the net heat exchanged 
between two brick surfaces is less than that exchanged between two 
sooted surfaces at the same temperatures. The ratio of the two 
quantities of the net heat exchanged is here called the "coefficient 



22 



FLOW OF HEAT THROUGH FURNACE WALLS. 



of net heat exchange." The latter increases with the absolute 
temperature of the surfaces. For the brick surfaces this coefficient 
at 700° C, absolute, is perhaps 0.5; that is, two brick surfaces will 
exchange only about 0.5 of the net amount of heat exchanged 
between two sooted surfaces which are at the same respective tem- 
peratures as the brick surfaces. 

The conditions existing between the two surfaces of an air space in 
a furnace wall are very nearly like those shown in figure 13. The 

two surfaces of the air space are ex- 
posed to nothing excepting to one 
another^ 

By multiplying the values of the 
constant C as given on page 20 by 
this coefficient for brick, formula (I) 
can be applied directly to compute 
the heat radiated across an &ir space, 
or the same results can be obtained 
if the values of H figured for sooted 
surfaces are multiplied by 0.5. 

Figuring the net heat radiated be- 
tween any two surfaces by formula 
(I) is rather cumbersome; therefore 
figures 15 to 18, inclusive, have been 
worked out to give the net heat radi- 
ated from one sooted surface to another, and satisfy in all 
instances the conditions that are shown by figures 12 and 13. To 
obtain the net radiation between any other substances the values of 
H obtained from the charts are multiplied by the proper coefficients 
of net heat exchange, which in all cases are less than 1.00. Fig- 
ures 15 and 16 are worked out in metric and figures 17 and 18 
in English units. Figure 15 is a part of figure 16 on a larger 
scale, the range of the former being limited to the portion of the 

Cold surface at T2 




Figure 12.— Radiation of heat from hot 
spheroidal surface to inclosing cooler surface. 



-180 



J^°^ 



y 



Hot surface atTi 



Figure 13.— Radiation of heat from infinite hot plane surface to infinite cooler 

plane surface. 

latter below the heavy broken line. In like manner figure 17 is 
a part of figure 18 on a larger scale, the part below the 500° F. line. 
To illustrate the use of the charts, let it be required to find the 
radiation from a sooted surface at 700° C. absolute (427° C. on the 
ordinary scale) to a sooted surface at 550° C. absolute (277° C. 
ordinary scale). Turn to figure 15. At the foot of the chart is the 
absolute temperature of the cooler surface in degrees centigrade. 



DISCUSSION OF PHYSICAL LAWS. 23 

Take the vertical line starting from a temperature point of 550° C. 
and follow it to the curve labeled 700° C. This is the temperature of 
the hotter surface. From the intersection of the vertical line with 
the curve draw a horizontal line to the scale on the left hand, which 
scale indicates that in the assumed case the radiation is 11 small 
calories per minute per square centimeter of the hot surface. If 
the radiation for brick surfaces not sooted is wanted, multiply 11 
by 0.5, say; the result is 5.5 calories, which is the approximate net 
radiation from 1 square centimeter of the hotter brick surface when 
its absolute temperature is 700° C. and that of the cooler surface is 
550° C. 

Again, suppose that it is desired to know the radiation from a sooted 
surface at 1,600° C. to a sooted surface at 1,200° C. At the foot 
of figure 16 take the vertical line 
starting from 1,200° C, follow it 
until the curve of 1,600° C. is 
reached, and then follow the hori- 
zontal line passing through the in- 
tersection point to the scale on the 
left; the scale indicates that in 
the given case the net radiation is 
340 calories per square centimeter — 
of the hotter surface. If the radi- // 

ation from a brick Surface Under Figure 14.-Radiation of heat from infinite hot 
. , „ . , . . . . , plane surface to convex surface. 

the ioregomg conditions is wanted, 

multiply 340 by 0.5, and the result is 170 calories for brick not sooted. 
To take a more specific example, use figures 17 and 18 in figuring 
the rate of heat radiation across the air space in the side wall of the 
long-combustion chamber for test No. 16. For the temperatures of 
the surfaces, take the average temperatures of the highest gradients 
of figures 6, 8, and 10; that is, those gradients which represent equi- 
librium of temperature. From the three figures it is found that the 
average temperature indicated by the three thermocouples embedded 
near the hotter surface of the air space is 514° C, ordinary scale, or 
1,418° F. on the absolute scale, and the average of the indications 
of the three couples embedded near the colder surface is about 408° C, 
ordinary scale, or 1,227° F., absolute scale. We have then: 

T 1 = 1,418°F. 
and T 2 = 1,227° F. 

a It should be remembered, however, that in the experiments discussed the junctions of the thermo- 
couples were embedded in the brick about 1 inch from the surface, and therefore the assumed tempera- 
tures are farther apart than the actual temperatures were. 

Necessarily, higher values of the net heat exchanged or radiated will result when these assumed tem- 
peratures are used in computation. The exact location of the junctions of the thermocouples could not be 
determined, and therefore no accurate and reliable correction of the surface temperatures can be made. 




24 



FLOW OF HEAT THROUGH FURNACE WALLS. 



70 



60 



The net radiation corresponding to these temperatures can be found 
approximately from figure 17 in the following manner: 

On the scale at the foot of the chart locate the temperature of 
1,227° F., absolute, the temperature of the colder surface. This 
temperature will be found between the points of 1,200° and 1,300° 
F. After locating this point, follow an imaginary vertical line rising 
from it and cutting the curve of 1,418° F. This curve, though not on 

the chart, can be imag- 
ined in its proper place 
between the curves of 
1,400° and 1,500° F. 
From the intersection of 
the two imagined lines, 
draw a horizontal line to 
the scale on the left, 
which gives the heat in 
British thermal units 
radiated per minute per 
square foot of the hot- 
ter surface. In the case 
under consideration, the 
radiated heat is found 
to be 44 B. t. u. for 
sooted surfaces. The 
radiation for brick sur- 
faces is obtained by mul- 
tiplying 44 by the coef- 
ficient of heat exchange 
for brick, which is taken 
as 0.5. The radiation 
for the brick is then 
44X0.5 = 29 B. t. u. 

Now, the wall is 40 
feet long and 4 feet 
high, which makes the 
total radiating surface 
40X4 = 160 square feet, and the total radiation through the space in 
one side wall is 160X22 = 3,520 B. t. u. 

THE LAW OF HEAT CONDUCTION. 



80 

Ofl 
WW 

£ H 

£ c 

oo 

OQOQ 

O WW 
W£t> 

Hg^50 

ggtf 40 
w ^O 

<&z 

1-4 P-iEH 
fi§«! 30 

*§§ 

So« 

OHP20 

ge 

H« 



10 



































































J 
















































^ 














— \ 


fr 
































'OO 














\° 


o 
































\\ 


n 


















































<?> 
















































d 
















































% 
















































^ 












































































































































































































































































Mi)- 














































































I 
















































































































































































































































1 


































































































i 












800 
















































































\ 
































































































































































































1 


































































7( 


)0 


D 








































































































































































1 














600° 


























1 
















1 [ 












































500 

i i 















































1— 












































400° 


































1 










• 300^ 









































°0 200 400 600 800 1000 1200 

ABSOLUTE TEMP.,°G., OF SOOTED SURFACE 

ABSORBING NET HEAT RADIATED 

BY HOTTER SURFACE. 

Figure 15.— Radiation from a hot surface to an infinite cooler 
surface at various temperatures; relations expressed in the metric 
system of units. 



The law governing the travel of heat by conduction is simpler 
than the law of heat travel by radiation and is well known and much 
used by engineers. 

The amount of heat conducted through a unit of area from one 
part of a body to another is proportional to the temperature dif- 



DISCUSSION OF PHYSICAL LAWS. 25 

ference of the two parts, proportional to the conductivity of the 
body, and also inversely proportional to the distance between the 
two parts of the body. This law is expressed by the following 
equation : 

(2) H = |(T 1 -T 2 ) 

Where H = the quantity of heat conducted per unit of area per unit of 
time. 
c = the conductivity of the material, which varies some- 
what with the temperature. 
d = ihe distance between the two parts of the body. 
T x = the temperature of the hotter part. 
T 2 = the temperature of the colder part. 
The experiments made by J. K. Clement and W. L. Egy a at the 
University of Illinois engineering experiment station show the con- 
ductivity of fire brick at 700° C. to be about 0.0024 in the metric 
units, which is equivalent to 0.1158 B. t. u. per square foot per 
minute per 1° F. difference of temperature when the distance between 
the two heat-exchanging planes is 1 inch. 

This conductivity being known formula (2) can be used to figure 
out the quantity of heat passing by conduction through the fire brick 
portion of the side wall for the test No. 16, and this quantity of heat 
can be compared with that radiated across the space, as computed on 
page 24. For T x take the average of the three temperatures 1 inch 
(about) from the furnace as given by the highest three gradients of 
figures 6, 8, and 10, and for T 2 take the average of the corresponding 
three temperatures 1 inch from the air space of the fire-brick side. 
The values are: 

T 1 = 962°C. = 1,763°F. ; 
T 2 = 516°C.= 960° F., 
and d = 7 inches. 

Substituting the above values in equation (2) gives 

TX 0.1158 X (1763-960) 1QQT3 , 

H = — s— =13.3 B. t. u. per square 

foot of the wall. 

For one whole side it will be 

13.3 X 40 X 4 = 2,128 B. t. u. 

The heat radiated across the air space was calculated to be 3,520 
B. t. u. 

Hence, the temperatures used in both calculations being regarded 
as in equilibrium, the two heats should be equal if the temperatures 
were correct. However, it is known, and has already been stated, that " 

a University of II inois Bull. No. 36. 



26 



FLOW OF HEAT THROUGH FURNACE WALLS. 



the temperatures of the radiating surfaces of the air space as used in 
the calculation were only approximate, and that they were farther 
apart than the temperatures of the surfaces actually were. This is 
the reason why the result of the computation of heat radiated across 
the space is too high. If allowance is made for this inaccuracy of data 
and for the fact that the coefficient of net heat exchange could only 
be approximated from the meager experimental data that is at pres- 
ent available on this subject, the agreement between the amount of 



H 800 

< 

cctf 
pgTOO 

£g 

ggeoo 

gg 

^500 

m 

Ph 

QO300 

HO 
E-ioq 

3h 

<K 
tf«J200 

H>H 

si 

gSioo 

(-Jt- 1 
<o 

























r 


*■ 










| 




































































uifl&- 
















































































^ 
















































































^* 


%> 
















































































<-<$>.' \ 










































































































































































































































































































1 


70 


0^" 








































































































































































































































































































































































































































































































































































i 


"or 


c 


























































































































































































































































































































































































































































































"1500°" 




























































































































\ 
















































































\ 
















































































\ 






























" 


uc 


0° 
























































































































































































































































































































isnc 


1° 
















































































































\ 














































































\ 


\ 








































IBOf 







































\ 








































| 






































s 


\ 






































L100 c 


_, 






































\ 












































































\ 


\ 


































" 


Of 


0° 








































\ 














\ 
































































\ 


i 












\ 
















- 800- 


9C 


0°| — 










































\ 












\ 
















I 1 


/U 


j4— 




















""> 


s 




















\ 












\ 











£ 200 400 600 800 1000 1200 1400 1600 1800 2000 

fc ABSOLUTE TEMPERATURE,°C., OF SOOTED SURFACE ABSORBING NET HEAT 

RADIATED BY HOTTER SURFACE. 

Figure 16.— Radiation of heat from a hot surface to an infinite cooler surface at various temperatures; 
relations expressed in the metric system of units. 

heat radiated across the air space and that conducted through the fire- 
brick wall is better than might be expected. The agreement further 
shows that the losses of heat by radiation could be figured out in an 
entirely rational way if more were known about the radiating prop- 
erties of fire brick and similar material. 

It may be stated here that in the specific case of the two given 
methods of calculating the amount of heat passing through the side 
wall, the method of calculation by the law of conduction is the more 
accurate and the more reliable one, because the data for it are more 



DISCUSSION OF PHYSICAL LAWS. 27 

accurate, and any errors in temperature are not raised to the fourth 

power, as they are in calculating by the law of radiation. 

It will be interesting to figure out the total heat lost through the 

walls, roof, and bottom of the furnace by the methods of conduction. 

From previous calculation the loss through both side walls for test 

No. 16 was 

2,128 X 2 = 4,256 B. t. u. 

The average temperature drop through the fire-brick portion of the 
roof when the temperatures were in equilibrium was from 787° to 
420° C., or from 1,449° to 788° F. 

Substituting these values in equation (2) gives: 

tt Q.H58X (1,449-788) 1AO _ T ,, f ' p ., , 

H = 4 = 10.95 B. t. u. per square loot ol the root. 

Now, the roof was 40 feet long and the fire-brick portion about 4 
feet wide, which makes the total area 

40X4 = 160 square feet 

and the total heat lost through the roof 

160 X 10.95 = 1,752 B. t. u. per minute. 

On the assumption that the heat lost through the bottom of the 
furnace is about equal to that lost through the roof, the total heat 
lost from the furnace by dissipation through the walls, roof, and 
bottom is 

2 X2,128 + 1,752 + 1,752 = 7,760 B. t. u. per minute. 

The rate of combustion was about 900 pounds of coal per hour or 

15 pounds per minute. If each pound of coal developed 12,000 
B. t. u., the total quantity of heat passing through the furnace per 
minute was 

12,000 X 15 = 180,000 B. t. u. 

Of this heat yloro o o" = 4.3 per cent is lost in dissipation through the 
walls, roof, and bottom of the furnace. Probably 1.5 to 2 per cent 
of the total loss or nearly half the proportional loss could be avoided 
by proper selection of material and proper furnace-wall construction. 

COMPARISON OF THE LAWS. 

So far the law of radiation and the law of conduction have been 
discussed and illustrated separately. It remains to compare or 
contrast these laws so as to bring out more prominently the influence 
of the fourth power in the radiation law. Figure 19 has been devised 
to show such contrast. The upper curve shows how the amount of 
heat radiated from one sooted surface to another at a constant 
temperature difference of 100° C. or 180° F. increases as their tem- 
peratures rise. The scale at the foot of the chart gives the absolute 



28 



FLOW OF HEAT THKOTJGH FURNACE WALLS. 



500 
CO 

CQH 480 
Ptf 

Op 

440 



460 



420 



400 



300 



260 



temperature of the hotter surface in degrees centigrade, the scale 
at the top gives the same in degrees Fahrenheit, the scale at the 
left gives the net heat exchanged between the two surfaces in metric 
units, while the scale on the right gives the same in English units. 

Let it be assumed 
that the hotter sooted 
surface is at 500° C, ab- 
solute, and the colder at 
400° C, absolute; the 
net heat exchanged be- 
tween the surfaces can 
be found by following 
the vertical line of 500° 
C. until it cuts the curve, 
and then from this in- 
tersection following the 
horizontal line to the 
left or the right scale, 
according to whether 
the net heat is desired in 
metric or English units. 
The assumed condition 
gives about three calo- 
ries. When the temper- 
ature of the hotter sur- 
face is doubled, the dif- 
erence between the two 
surfaces remaining 100° 
C. or 180° F., the heat 
exchanged increases to 
26 calories, or nearly 
nine times as much as 
in the first case. 

The lower curve shows 



the approximately sim- 
ilar relation between 
two surfaces not sooted. 
The conditions for both 
curves must be those of 
figures 12 and 13. 
The upper horizontal line at the foot of the figure shows the rela- 
tion of the heat transmitted by conduction through a 2-inch brick 
wall and the temperatures of the two surfaces of the brick wall when 
the difference of the temperatures remains constantly equal to 100° C. 
or 180° F. The curve shows that the heat transmitted through the 



EnpJ 

© , 

W£: 380 

Po 

- M 360 
£ 340 

o o 

<» <J 320 

°B 

Eh cq 

fe ft 280 

O .J 
^ M 240 

oh 24U 

PS Ct5 

&• P3 220 

ggiso 

QH 140 

H O 

<\ H 120 

l-H 

ft CO 
«<H 100 

.P 

Ph 



160 



80 



60 



Is 



40 



20 































































































































A 
"* 
























































































* 






\ 


% 








































b\ 




















































■< 












































































&A- 
































































^ 














V 
































1 


% 














^ 


















































































































































































































































| 




































§ 
















































fc 


































































































































































1 


















































\ 
















" 


8C 


o c 


























\ 












































\ 




I 












































\ 














































\ 


\ 














































\ 




1 












































\ 




















1700° 
























\ 




\ 


' 










































\ 


1 


\ 






























































































\ 
















































\ 


1 


















1 


iti 


JU 
















































































l 






























































































I 


















_J 


LOt 


'0 














































































\ 






























































1400° 
































—1 












































































































-1300° 




































| 












1 












































-120 

i 


n 






U 












































_no 


C 




























\ 










































\ 






' 










1000-° 






= pnn° 


J0£ 


J - 
























\ 


















. 


























1 




1 











ABSOLUTE TEMP.,°F., OF SOOTED SURFACE 
ABSORBING NET HEAT RADIATED BY 
HOTTER SURFACE. 
Figure 17. — Radiation of heat from a hot surface to a cooler sur 
face; relations expressed in British thermal units, degreesFahren- 
heit, and square feet. 



DISCUSSION OF PHYSICAL LAWS. 



29 



brick remains constant no matter what the temperatures of the sur- 
faces are, so long as the temperature difference remains equal to 
100° C. 

The lower horizontal straight line shows the same relation for a 
brick wall 4 inches thick. The heat passing through the 4-inch 



5000 



m 

P 
o 

H 

m 

D 

< 

00 ^ 

fig 

o ^ 

GG S 

o ^ 

PH 

El 

En 

O 

o 

GG 



o 

S P5 



4500 



4000 



3500 



3000 



2500 



2000 



1500 



<ri W 
" D-i 



1000 



500 









— \ 
-7 


— 
f 


1 1 1 
37nn° v 


a 


ib. 


50] 








































































ute. 




































































































-^ 


\* 




'J^ 




-^ 




































































%\ 








































































°\ 




c 


V 




























-E 


60 


0° 






































































































































































































































































































































































































. 350C 












































































































































































































































































































































































































34UI 


J 






























































































































































































































































































































































































































































\ 






























































































































32nn° 














































































































































































































































tOC 


°- 


























































































































































































































































































































°- 














ol 


;ul 














































\ 


\ 














































































\ 






























290( 


° 














































> 


V 














































































\ 














\ 














1 , 


















































\ 














\ 














2800"" 














































\ 














\ 














1 | 






























































\ 














2700° 




























































\ 














I | 












































































2600° 
































































| 












1 1 
































































\ 












_l 1 






























































\ 


\ 












240C 


° 






























































\ 


\ 






-2300" 
































































\ 


\ 






| | 


220( 


)°- 






































































-21C 

i, 


H)° 


J- 


































































1 


I 


j—1.2 


00 

j 


f- 

J — 

■\0 


































































\ 




-1900 U r- 
































































\ 


I 




^ToF-SSl^ 














































\ 


















\ 






=1500? 


=iow - 














































\ 


















\ 


\ 




| 




' 1400° _ 














































\ 


' 
















' 


1 



FlGUKE 18. 



ABSOLUTE T.EMP., F., OF SOOTED SURFACE ABSORBING NET HEAT 
RADIATED BY HOTTER SURFACE. 

-Radiation of heat from a hot surface to a cooler surface; relations expressed in British 
thermal units, degrees Fahrenheit, and square feet. 



wall is one-half of that passing through the 2-inch wall, which, of 
course, might be expected. The chart shows that the curves of 
radiation start below the lines of conduction, but as the temperatures 
increase both of the radiation curves cross the lines of conduction 
and beyond that rise very rapidly. 



30 



FLOW OF HEAT THKOUGH FURNACE WALLS. 



APPLICATION OF THE LAWS. 

The chart further shows that an air space is more advantageous 
than a 2-inch brick wall if the temperature of the hotter surface is 
below 625° C, absolute, or 565° F., ordinary scale, but above that 
temperature the brick wall is better. With a 4-inch wall the limit- 
ing temperature drops down to 500° C, absolute, or 440° F., ordinary 











360 




ABSOLUTE TEMPERATURE 
720 1080 1440 1800 


OF HOTTER SURFACE 
2160 2520 2880 


U F 




3240 








50 




































































































































/ 


















































































/ 


















































































1 
































45 




































































































































































































































































































































M 
















































/ . 














































































° i 














































































o 

CD 






























































































































































/£? 














































































/£ 


































35 














































' £ 














































































/ 






































P 












































/ 
















































































/ 














































































J& 




































W 30 






























































































































































































































































































































g25 










































' c 

"*5 




























































































































































a 








































14 

M 








































I r 


3 








f^f 






























§ 








































- c 
o 










1? 
































ft 

g20 
















































Q' 






































































f - 

1) 
J 








/4 






































































/ c 








































B 






































'a 










o 


































o 






































o 
9 






































hJ 




































1 








If 




































S" 




































+3 








' a 




































































/ 








/« 


s j 






































ti 


































/ < 


9 






/ 

3 








































o 

< 


































no 












































































1 


e? 






As 








































°io 
































'4 


t 














































































z> 






fl 








































































'S 








9 








































































/ 


6 




/& 
















































































W 3 
















































5 
































/ * 


V 






























































































































































Calories conducted through 2 inches of fire brick. 
































































































-' 






















































































































































184.5 



166.0 



147.6 



129.1 



110.7 



92.2 



73.8 



55.3 



CM 
H 

CO 

O 

i-l 

t» 
En 

w 



36.9 



18.4 



3.69 



1800 



2000 



200 400 600 800 1000 1200 1400 1600 

ABSOLUTE TEMPERATURE OF HOTTER SURFACE. °C. 
Figure 19.— Comparison of laws of heat radiation and heat conduction. 

scale. If asbestos, ash, or other better insulating materials were 
used in place of the brick, this limiting or dividing temperature 
would fall still lower. These statements hold particularly for the 
condition of 100° C. temperature difference. There is one lesson 
which the chart brings out rather emphatically and that is ; when 



PUBLICATIONS ON FUEL TESTING. 31 

heat at low temperature is to be insulated, use air space; when the 
heat is at high temperature, as is the case in furnaces, use solids 
of poor heat conductivity. That the space is less effective at high 
temperatures than at low ones is known to the makers of "thermos" 
bottles, who advertise that such bottles keep liquids cold 72 hours 
and keep liquids hot 24 hours. 

PUBLICATIONS ON FUEL TESTING. 

The following publications, except those to which a price is affixed, 
can be obtained free by applying to the Director of the Bureau of 
Mines, Washington, D. C. The priced publications can be purchased 
from the Superintendent of Documents, Government Printing Office, 
Washington, D. C. : 

PUBLICATIONS OP THE UNITED STATES GEOLOGICAL SURVEY. 

Bulletin 261. Preliminary report on the operations of the coal-testing plant of 
the United States Geological Survey at the Louisiana Purchase Exposition, in St. 
Louis, Mo., 1904; E. W. Parker, J. A. Holmes, M. R. Campbell, committee in charge. 

1905. 172 pp. 10 cents. 

Professional Paper 48. Report on the operations of the coal-testing plant of 
the United States Geological Survey at the Louisiana Purchase Exposition, St. Louis, 
Mo., 1904; E. W. Parker, J. A. Holmes, M. R. Campbell, committee in charge. 1906. 
In three parts. 1492 pp., 13 pis. $1.50. 

Bulletin 290. Preliminary report on the operations of the fuel-testing plant of 
the United States Geological Survey at St. Louis, Mo., 1905, by J. A. Holmes. 1906. 
240 pp. 20 cents. 

Bulletin 323. Experimental work conducted in the chemical laboratory of 
the United States fuel-testing plant at St. Louis, Mo., January 1, 1905, to July 31, 

1906, by N. W. Lord. 1907. 49 pp. 10 cents. 

Bulletin 325. A study of four hundred steaming tests made at the fuel-testing 
plant, St. Louis, Mo., 1904, 1905, and 1906, by L. P. Breckenridge. 1907. 196 pp. 
20 cents. 

Bulletin 332. Report of the United States fuel-testing plant at St. Louis, Mo., 
January 1, 1906, to June 30, 1907; J. A. Holmes, in charge. 1908. 299 pp. 25 cents. 

Bulletin 334. The burning of coal without smoke in boiler plants; a preliminary 
report, by D. T. Randall. 1908. 26 pp. 5 cents. (See Bull. 373.) 

Bulletin 336. Washing and coking tests of coal and cupola tests of coke, by 
Richard Moldenke, A. W. Belden, and G. R. Delamater. 1908. 76 pp. 10 cents. 

Bulletin 339. The purchase of coal under government and commercial speci- 
fications on the basis of its heating value, with analyses of coal delivered under gov- 
ernment contracts, by D. T. Randall. 1908. 27 pp. 5 cents. (See Bull. 428.) 

Bulletin 343. Binders for coal briquettes, by J. E. Mills. 1908. 56 pp. 

Bulletin 362. Mine sampling and chemical analyses of coals tested at the United 
States fuel-testing plant, Norfolk, Va., in 1907, by J. S. Burrows. 1908. 23 pp. 
5 cents. 

Bulletin 363. Comparative tests of run-of-mine and briquetted coal on locomo- 
tives, including torpedo-boat tests and some foreign specifications for briquetted fuel, 
by W. F. M. Goss. 1908. 57 pp., 4 pis. 

Bulletin 366. Tests of coal and briquettes as fuel for house-heating boilers, by 
D. T. Randall. 1908. 44 pp., 3 pis. 

Bulletin 367. Significance of drafts in steam-boiler practice, by W. T. Ray and 
Henry Kreisinger. 1909. 61 pp. 



32 FLOW OF HEAT THROUGH FURNACE WALLS. 

Bulletin 368. Washing and coking tests of coal at Denver, Colo., by A. W. Belden 
G. R. Delamater, and J. W. Groves. 1909. 54 pp., 2 pis. 

Bulletin 373. The smokeless combustion of coal in boiler plants, by D. T. Randall 
and H. W. Weeks. 1909. 188 pp. 20 cents. 

Bulletin 378. The purchase of coal under government specifications, by J. S. 
Burrows. 1909. 44 pp. 10 cents. (See Bull. 428.) 

Bulletin 382. The effect of oxygen in coal, by David White. 1909. 78 pp. 
3 pis. 

Bulletin 385. Briquetting tests at the United States fuel-testing plant, Norfolk, 
Va., 1907-8, by C. L. Wright. 1909. 41 pp., 9 pis. 

Bulletin 392. Commercial deductions from comparisons of gasoline and alcohol 
tests on internal-combustion engines, by R. M. Strong. 1909. 38 pp. 5 cents. 

Bulletin 393. Incidental problems in gas-producer tests, by R. H. Fernald, C. D. 
Smith, J. K. Clement, and H. A. Grine. 1909. 29 pp. 5 cents. 

Bulletin 402. The utilization of fuel in locomotive practice, by W. F. M. Goss. 
1909. 28 pp. 

Bulletin 403. Comparative tests of run-of-mine and briquetted coal on the tor- 
pedo boat Biddle, by Walter T. Ray and Henry Kreisinger. 1909. 49 pp. 10 cents. 

Bulletin 412. Tests of run-of-mine and briquetted coal in a locomotive boiler, 
by Walter T. Ray and Henry Kreisinger. 1909. 32 pp. 

Bulletin 416. Recent development of the producer-gas power plant in the United 
States, by R. H. Fernald. 1909. 82 pp., 2 pis. 15 cents. Reprinted as Bureau of 
Mines Bulletin 9. 

Bulletin 428. The purchase of coal by the Government under specifications, with 
analyses of coal delivered for the fiscal year 1908-9, by G. S. Pope. 80 pp. 10 cents. 
Reprinted as Bureau of Mines Bulletin 11. 

PUBLICATIONS OF THE BUREAU OF MINES. 

Bulletin 1. The volatile matter of coal, by H. C. Porter and F. K. Ovitz. 1910. 
56 pp., 1 pi. 

Bulletin 2. North Dakota lignite as a fuel for power plant boilers, by D. T. Ran- 
dall and Henry Kreisinger. 1910. 42 pp., 1 pi. 

Bulletin 3. The coke industry of the United States as related to the foundry, by 
Richard Moldenke. 1910. 32 pp. 

Bulletin 4. Features of producer-gas power-plant development in Europe. 1911. 
27 pp., 4 pis. 

Bulletin 5. Coking and washing tests of coal at Denver, Colo., July 1, 1908, to 
June 30, 1909, by A. W. Belden, J. W. Groves, and K. M. Way. 1910. 62 pp. 

Bulletin 6. Coals available for illuminating-gas manufacture, by A. H. White 
and Perry Barker. 1911. 

Bulletin 7. Essential factors in the formation of producer-gas, by J. K. Clement, 
L. H. Adams, and C. N. Haskins. 1911. 

o 



